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Question 1

Newton’s law of gravitation:

Answer 1

F = (G x M x m)/d^2

Question 2

The eccentricity of an ellipse is given by:

Answer 2

e = (F x F’)/2a

In terms of the semi-major axis, a, and the semi-minor axis, b, we have:
e = √ (1 - (b/a)^2)

Question 3

Perihelion:

Answer 3

When the planet is on the major axis at the point nearest F

Question 4

Aphelion:

Answer 4

When the planet is on the major axis at the point farthest from F

Question 5

Kepler’s First Law:

Answer 5

Planets orbit in ellipses, with the Sun at one focus.

Question 6

Kepler’s Second Law:

Answer 6

The product of the distance from the focus and the transverse velocity is a constant. The transverse velocity is the velocity perpendicular to a line drawn from the object to the focus. As a hint for working problems, consider that when a planet is at aphelion or perihelion (farthest and closest to the Sun), ALL of the velocity is transverse. An alternative statement is that the line from the planet to the Sun sweeps out equal areas in equal periods of time.